Momentum-dependent electron-phonon coupling in charge density wave systems

Pouget, Jean-Paul [Laboratoire de Physique des Solides, CNRS UMR 8502, Université de Paris-Sud, Université Paris-Saclay, 91405 Orsay, France] Canadell, Enric [Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus Bellaterra, 08193 Barcelona, Spain] Guster, Ionel-Bogdan [UCL]

Many charge density wave (CDW) systems exhibit q(T) electron-hole modulations continuously varying with T and saturating upon cooling at an incommensurate value even if the maximum occurring in the electron-hole Lindhard response does not exhibit such a thermal shift. Using a simple RPA argument we show that the experimental q(T) can be understood if the electron-phonon coupling (EPC) g(q), necessary to set coupled electronic and structural modulations, is momentum dependent. In this analysis, the sense of variation of q(T) depends upon the sign of ∂g(q)∂q and its amplitude of thermal variation is controlled by the electron-hole coherence length (or CDW rigidity) in the modulation direction. This model quantitatively accounts for the thermal dependence of q(T) in the one-dimensional (1D) CDW system K0.3MoO3 (blue bronze) both in its CDW ground state and in its pretransitional CDW fluctuation regime. We suggest that such a general analysis can be extended to account for the q(T) dependence observed in other 1D and 2D CDW systems such as the transition metal di- and trichalcogenides as well as the lanthanide and rare-earth tritellurides. Using a detailed analysis of the low frequency phonon spectrum of the blue bronze, we then propose a new scenario for the q dependent EPC, where g(q) is due to a momentum-dependent hybridization between the critical phonon branch bearing the Kohn anomaly and other low-lying phonon branches. This allows obtaining a sign of ∂g(q)∂q in agreement with that deduced from the analysis of q(T). Finally, we propose that similar hybridization effects could also be relevant for other 1D and 2D CDW systems exhibiting a thermally dependent modulation.